projective line

Noun

projective line (plural projective lines)

1. (projective geometry) A line that includes a point at infinity; a line in a projective space; a projective space of dimension 1.
   • A projective line in P²( R ), consists of the projective points defined by coplanar directions in R ³.
     In other words, just as the points in P²( R ) correspond to one-dimensional subspaces in R ³, the projective lines correspond to two-dimensional subspaces in R ³.2007, Unnamed translator, Ana Irene Ramírez Galarza, José Seade, Introduction to Classical Geometries, [2002, Introducciòn a la Geometria Avanzada], Springer (Birkhäuser), page 97, In P2( R ), the...
   • Consider the projective line mathbf P¹, with homogeneous coordinates x and t and open sets U_0(x ne 0) and U_1(t ne 0).2008, Catriona Maclean (translator), Daniel Perrin, Algebraic Geometry: An Introduction, [1995, D. Perrin, Géométrie algébrique] Springer, page 37

   Synonyms:

   projective straight line